We study slow-roll inflation with a Gauss-Bonnet term that is coupled to an inflaton field nonminimally. We investigate the inflationary solutions for a specific type of the nonminimal coupling to the GaussBonnet term and inflaton potential both analytically and numerically. We also calculate the observable quantities such as the power spectra of the scalar and tensor modes, the spectral indices, the tensor-to-scalar ratio, and the running spectral indices. Finally, we constrain our result with the observational data by Planck and BICEP2 experiment.

We identify the dual geometry of the hadron phase of dense nuclear matter and investigate the confinement/deconfinement phase transition. We suggest that the low temperature phase of the RN black hole with the full backreaction of the bulk gauge field is described by the zero mass limit of the RN black hole with hard wall. We calculated the density dependence of critical temperature and found that the phase diagram closes. We also study the density dependence of the ρ meson mass. *

We explicitly construct Green functions for a field in an arbitrary representation of gauge group propagating in noncommutative instanton backgrounds based on the ADHM construction. The propagators for spinor and vector fields can be constructed in terms of those for the scalar field in noncommutative instanton background. We show that the propagators in the adjoint representation are deformed by noncommutativity while those in the fundamental representation have exactly the same form as the commutative case.

We construct twisted quantum bundles and adjoint sections on noncommutative T 4 , and investigate relevant D-brane bound states with non-Abelian backgrounds. We also show that the noncommutative T 4 with non-Abelian backgrounds exhibits SO(4, 4|Z) duality and via this duality we get a Morita equivalent T 4 on which only D0-branes exist. For a reducible non-Abelian background, the moduli space of D-brane bound states in Type II string theory takes the form a (T 4 ) qa /S qa .

We construct the consistent CP (n) model on noncommutative plane. The Bogomolny bound on the energy is saturated by (anti-)self-dual solitons with integer topological charge, which is independent of their scaling and orientation. This integer quantization is satisfied for our general solutions, which turns out regular everywhere. We discuss the possible implication of our result to the instanton physics in Yang-Mills theories on noncommutative R 4 .